控制系统的MATLAB仿真与设计课后答案>>z=-4*sqrt(2)*sin(t);>>plot3(x,y,z,'p');>>title('Line in 3-D Space');>>text(0,0,0,'origin');>>xlabel('X'),ylable('Y'),zlable('Z');grid;4>>theta=0:0.01:2*pi;>>rho=sin(2*theta).*cos(2*theta);>>polar(theta,rho,'k');5>>[x,y,z]=sphere(20);>>z1=z;>>z1(:,1:4)=NaN;>>c1=ones(size(z1));>>surf(3*x,3*y,3*z1,c1);>>hold on>>z2=z;>>c2=2*ones(size(z2));>>c2(:,1:4)=3*ones(size(c2(:,1:4)));>>surf(1.5*x,1.5*y,1.5*z2,c2);>>colormap([0,1,0;0.5,0,0;1,0,0]);>>grid on>>hold off第四章1>>for m=100:999m1=fix(m/100);m2=rem(fix(m/10),10);m3=rem(m,10);if m==m1*m1*m1+m2*m2*m2+m3*m3*m3disp(m)endend2M文件：function[s,p]=fcircle(r)s=pi*r*r;p=2*pi*r;主程序：[s,p]=fcircle(10)3>>y=0;n=100;for i=1:ny=y+1/i/i;end>>yfunction f=factor(n)if n<=1f=1;elsef=factor(n-1)*n;end主程序：>>s=0;for i=1:5s=s+factor(i);end>>s5>>sum=0;i=1;while sum<2000sum=sum+i;i=i+1;end;>>n=i-26for循环M文件：function k=jcsum(n)k=0;for i=0:nk=k+2^i;end主程序：>>jcsum(63)While循环M文件：function k=jcsum1(n)k=0;i=0;while i<=nk=k+2^i;i=i+1;end主程序：>>jcsum1(63)第五章1>>A=[2,1,-5,1;1,-5,0,7;0,2,1,-1;1,6,-1,-4]; >>b=[13,-9,6,0]';>>x=A\bfunction f=fxyz(u)x=u(1);y=u(2);z=u(3);f=x+y.^2./x/4+z.^2./y+2./z;主程序：[U,fmin]=fminsearch('fxyz',[0.5,0.5,0.5])3>>X=linspace(0,2*pi,50);>>Y=sin(X);>>P=polyfit(X,Y,3)>>AX=linspace(0,2*pi,50);>>Y=sin(X);>>Y1=polyval(P,X)>>plot(X,Y,':O',X,Y1,'-*')4>>x=0:2.5:10;>>h=[0:30:60]';>>T=[95,14,0,0,0;88,48,32,12,6;67,64,54,48,41]; >>xi=[0:0.5:10];>>hi=[0:10:60]';>>temps=interp2(x,h,T,xi,hi,'cubic');>>mesh(xi,hi,temps);第六章1>>syms x>>y=finverse(1/tan(x))2>>syms x y>>f=1/(1+x^2); g=sin(y);>>fg=compose(f,g)3>>syms x>>g=(exp(x)+x*sin(x))^(1/2);>>dg=diff(g)4>>F=int(int('x*exp(-x*y)','x'),'y')5>>syms x>>F=ztrans(x*exp(-x*10))6>>a=[0 1;-2 -3];>>syms s>>inv(s*eye(2)-a);7>>f=solve('a*x^2+b*x+c')8>>f=solve('x+y+z=1','x-y+z=2','2*x-y-z=1')9>>y=dsolve('D2y+2*Dy+2*y=0','y(0)=1','Dy(0)=0') >>ezplot(y),grid on10>>a=maple('simplify(sin(x)^2+cos(x)^2);')11>>f=maple('laplace(exp(-3*t)*sin(t),t,s);')12>>syms t x>>F=sin(x*t+2*t); >>L=laplace(F)第七章1234 56 7第八章1-1>>h=tf([5,0],[1,2,2])1-2>>s = tf('s');>>H = [5/(s^2+2*s+2) ];>>H.inputdelay =21-3>>h=tf([0.5,0],[1,-0.5,0.5],0.1) 2>>num=2*[1,0.5];den=[1,0.2,1.01]; >>sys=tf(num,den)>>[z,p,k]=tf2zp(num,den);>>zpk(z,p,k)>>[A,B,C,D]=tf2ss(num,den);>>ss(A,B,C,D)3 >>num=[1,5]; den=[1,6,5,1]; ts=0.1; >>sysc=tf(num,den); >>sysd=c2d(sysc,ts,'tustin')4>>r1=1;r2=2;c1=3;c2=4;>>[A,B,C,D]=linmod('x84');>>[num,den]=ss2tf(A,B,C,D);>>sys=tf(num,den)5>>A=[1,1,0;0,1,0;0,0,2];B=[0,0;1,0;0,-2]; >>n=size(A)>>Tc=ctrb(A,B);if n==rank(Tc)disp('系统完全能控');elsedisp('系统不完全能控');end第九章1>>num=[2,5,1];den=[1,2,3];>>bode(num,den);grid on ;>>figure;>>nyquist(num,den);2>>num=5*[1,5,6];den=[1,6,10,8];>>step(num,den);grid on ;>>figure;>>impulse(num,den);grid on ;3>>kosi=0.7;wn=6;>>num=wn^2;den=[1,2*kosi*wn,wn^2];>>step(num,den);grid on ;>>figure;>>impulse(num,den);grid on ;4 M文件：function [rtab,info]=routh(den)info=[];vec1=den(1:2:length(den)); nrT=length(vec1);vec2=den(2:2:length(den)-1);rtab=[vec1; vec2, zeros(1,nrT-length(vec2))];for k=1:length(den)-2,alpha(k)=vec1(1)/vec2(1);for i=1:length(vec2),a3(i)=rtab(k,i+1)-alpha(k)*rtab(k+1,i+1);endif sum(abs(a3))==0a3=polyder(vec2);info=[info,'All elements in row ',...int2str(k+2) ' are zeros;'];elseif abs(a3(1))<epsa3(1)=1e-6;info=[info,'Replaced first element;'];endrtab=[rtab; a3, zeros(1,nrT-length(a3))];vec1=vec2; vec2=a3;end主程序：>>den=[1,2,8,12,20,16,16];>>[rtab,info]=routh(den)>>a=rtab(:,1)if all(a>0)disp('系统是稳定的');elsedisp('系统是不稳定的');end5>>num=7*[1,5];den=conv([1,0,0],conv([1,10],[1,1])); >>[gm,pm,wg,wc]=margin(num,den)第十章1 M文件：function varargout=rg_lead(ng0,dg0,s1)if nargout==1ngv=polyval(ng0,s1);dgv=polyval(dg0,s1);g=ngv/dgv;thetal=pi-angle(g);zc=real(s1)-imag(s1)/tan(thetal);t=-1/zc;varargout{1}=[t,1];elseif nargout==2ngv=polyval(ng0,s1); dgv=polyval(dg0,s1);g=ngv/dgv; theta=angle(g); phi=angle(s1);if theta>0phi_c=pi-theta;endif theta<0;phi_c=-thetaendtheta_z=(phi+phi_c)/2; theta_p=(phi-phi_c)/2;z_c=real(s1)-imag(s1)/tan(theta_z);p_c=real(s1)-imag(s1)/tan(theta_p);nk=[1 -z_c]; varargout{2}=[1 -p_c]; kc=abs(p_c/z_c);if theta<0kc=-kcendvarargout{1}=kc*nk;elseerror('输出变量数目不正确！');end主程序：>> ng0=[1]; dg0=10000*[1 0 -1.1772];>>g0=tf(ng0,dg0); %满足开环增益的为校正系统的传递函数>>s=kw2s(0.7,0.5) %期望的闭环主导极点>>ngc=rg_lead(ng0,dg0,s);>>gc=tf(ngc,1)>>g0c=tf(g0*gc);>>rlocus(g0,g0c);>>b1=feedback(g0,1); %未校正系统的闭环传递函数>>b2=feedback(g0c,1); %校正后系统的闭环传递函数>>figure,step(b1,'r--',b2,'b'); grid on%绘2M文件：function [ngc,dgc,k]=rg_lag(ng0,dg0,KK,s1,a)ngv=polyval(ng0,s1);dgv=polyval(dg0,s1);g=dgv/ngv;k=abs(g); %期望主导极点处的根轨迹增益beta=k/KK;[kosi1,wn1]=s2kw(s1);zc=-wn1*sin(a*pi/180)/sin(pi-atan(sqrt(1-kosi1^2)/kosi1)-(a*pi/180)) ; %利用正弦定理pc=beta*zc;ngc=beta*[1,-zc];dgc=[1,-pc];主程序：>>KK=20;s1=-2+i*sqrt(6);a=1>>ng0=[10];dg0=conv([1,0],[1,4]);>>g0=tf(ng0,dg0);>>[ngc,dgc,k]=rg_lag(ng0,dg0,KK,s1,a); >>gc=tf(ngc,dgc) >>g0c=tf(KK*g0*gc);>>b1=feedback(k*g0,1); >>b2=feedback(g0c,1); >>step(b1,'r--',b2,'b');grid on3M文件：function [ngc,dgc,k]=rg_lag(ng0,dg0,KK,s1,a)ngv=polyval(ng0,s1);dgv=polyval(dg0,s1);g=dgv/ngv;k=abs(g); %期望主导极点处的根轨迹增益beta=k/KK;[kosi1,wn1]=s2kw(s1);zc=-wn1*sin(a*pi/180)/sin(pi-atan(sqrt(1-kosi1^2)/kosi1)-(a*pi/180)); %利用正弦定理pc=beta*zc;ngc=beta*[1,-zc];dgc=[1,-pc];主程序：>>KK=128;s1=-2+i*2*sqrt(3);a=2>>ng0=[10];dg0=conv([1,0],conv([1,2],[1,8]));>>g0=tf(ng0,dg0);>>[ngc,dgc,k]=rg_lag(ng0,dg0,KK,s1,a); >>gc=tf(ngc,dgc) >>g0c=tf(KK*g0*gc);>>rlocus(g0,g0c);>>b1=feedback(k*g0,1); >>b2=feedback(g0c,1); >>figure,step(b1,'r--',b2,'b');grid on4M文件：function [ngc,dgc]=lead4(ng0,dg0,KK,Pm,w)[mu,pu]=bode(KK*ng0,dg0,w); [gm,pm,wcg,wcp]=margin(mu,pu,w);alf=ceil(Pm-pm+5); phi=(alf)*pi/180;a=(1+sin(phi))/(1-sin(phi)), dbmu=20*log10(mu);mm=-10*log10(a);wgc=spline(dbmu,w,mm), T=1/(wgc*sqrt(a)),ngc=[a*T,1]; dgc=[T,1];主程序：>>ng0=[1];dg0=conv([1,0,0],[1,5]);>>g0=tf(ng0,dg0);>>w=logspace(-3,3);>>KK=1;Pm=50;>>[ngc,dgc]=lead4(ng0,dg0,KK,Pm,w);>>gc=tf(ngc,dgc);g0c=tf(KK*g0*gc);>>bode(KK*g0,w);hold on,bode(g0c,w);grid on,hold off>>[gm,pm,wcg,wcp]=margin(g0c)>>Kg=20*log10(gm)>>g1=feedback(g0c,1);>>bode(g1),grid on,>>[mag,phase,w]=bode(g1);>>a=find(mag<=0.707*mag(1));>>wb=w(a(1))>>max(mag)>>b=find(mag==max(mag))>>wr=w(b)5M文件：function [ngc,dgc]=fg_lead_pm(ng0,dg0,Pm,w)[mu,pu]=bode(ng0,dg0,w); %计算原系统的对数频率响应数据[gm,pm,wcg,wcp]=margin(mu,pu,w); %求取原系统的相角裕度和剪切频率alf=ceil(Pm-pm+5); %计算控制器提供的最大超前角度，phi=(alf)*pi/180; %将最大超前角转换为弧度单位a=(1+sin(phi))/(1-sin(phi)); %计算a值dbmu=20*log10(mu); %系统的对数幅值mm=-10*log10(a); %wm处的控制器对数幅值wgc=spline(dbmu,w,mm); %差值求取wm，认为wm＝wc T=1/(wgc*sqrt(a)); %计算Tngc=[a*T,1]; dgc=[T,1];主程序：>>KK=40; Pm=50;>>ng0= KK *[1]; dg0=conv([1,0],conv([1,1],[1,4]));>>g0=tf(ng0,dg0) ;>>w=logspace(-2,4);>>[ngc,dgc]=fg_lead_pm(ng0,dg0,Pm,w)>>gc=tf(ngc,dgc),g0c=tf(g0*gc);>>b1=feedback(g0,1); b2=feedback(g0c,1);>>step(b1,'r--', b2,'b'); grid on>>figure, bode(g0,'r--',g0c,'b',w), grid on,>>[gm,pm,wcg,wcp]=margin(g0c), Km=20*log10(gm)。